Need help proving survivor function (difficult integration/proof)

Hello, I'm looking to prove a specific part of the survivor function. Basically, I need to show that the mean residual life function [m(t)] uniquely defines the distribution of T.

I have a solution, but I am not able to follow how the integration process leads to the final answer:

http://i993.photobucket.com/albums/a...ps37e58229.jpg

Here mrl(t) is the equivalent of m(t).

Re: Need help proving survivor function (difficult integration/proof)

Hey ishihara.

I'm not sure if this is useful, but the way I would attack this problem would be to treat it as an integro-differentiation problem. Basically what this involves is differentiating everything to get rid of the integral expression and the solve the DE that is left over.

If you have any extra tricks or results then by all means use them, but at the moment, this is all I can think of.